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if `P,Q` are two points on the line `3x+4y+15=0` such that `OP=OQ=9` then the area of triangle `OPQ` is

A

18 sq. units

B

`18sqrt(2)` sq. units

C

27 sq. units

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B

`OA = OB = 9, OD = (15)/(sqrt(25)) = 3`
`:. AB = 2AD = 2 sqrt(81-9) = 2 sqrt(72) = 12 sqrt(2)`
Hence `Delta = (1)/(2) (3 xx 12 sqrt(2)) = 18 sqrt(2)` sq. units.
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